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Discrete Fourier transform in arbitrary dimensions by a generalized Beevers–Lipson algorithm
Acta Crystallographica Section A Foundations of Crystallography, 2000The Beevers-Lipson procedure was developed as an economical evaluation of Fourier maps in two- and three-dimensional space. Straightforward generalization of this procedure towards a transformation in n-dimensional space would lead to n nested loops over the n coordinates, respectively, and different computer code is required for each dimension.
, Schneider, , van Smaalen S
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IEEE Transactions on Circuits and Systems I: Regular Papers, 2015
Real transforms require less complexity for computations and less memory for storages than complex transforms. However, discrete fractional Fourier and Hartley transforms are complex transforms. In this paper, we propose reality-preserving fractional versions of the discrete Fourier, Hartley, generalized Fourier, and generalized Hartley transforms. All
Wen-Liang Hsue, Wei-Ching Chang
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Real transforms require less complexity for computations and less memory for storages than complex transforms. However, discrete fractional Fourier and Hartley transforms are complex transforms. In this paper, we propose reality-preserving fractional versions of the discrete Fourier, Hartley, generalized Fourier, and generalized Hartley transforms. All
Wen-Liang Hsue, Wei-Ching Chang
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Fast Discrete Fourier Transform on Generalized Sparse Grids
2014In this paper, we present an algorithm for trigonometric interpolation of multivariate functions on generalized sparse grids and study its application for the approximation of functions in periodic Sobolev spaces of dominating mixed smoothness. In particular, we derive estimates for the error and the cost. We construct interpolants with a computational
Michael Griebel, Jan Hamaekers
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Journal of Pseudo-Differential Operators and Applications, 2020
The classical theorem of Titchmarsh says that the Fourier transform of a function from \(L^p(\mathbb R)\), \(1< p \le2\), that satisfies the Lipschitz \(\delta\)-condition with some ...
Radouan Daher, Othman Tyr
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The classical theorem of Titchmarsh says that the Fourier transform of a function from \(L^p(\mathbb R)\), \(1< p \le2\), that satisfies the Lipschitz \(\delta\)-condition with some ...
Radouan Daher, Othman Tyr
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Generalized Discrete Fourier Transform Based Minimization of PAPR in OFDM Systems
2014 International Conference on Computer and Communication Engineering, 2014Orthogonal frequency division multiplexing OFDM is a preferred technique in digital communication systems due to its benefits of achieving high bit rates and its ability to resist multipath effect over fading channels. However, high peak to average power PAPR ratio of the OFDM transmitted signal is a main drawback in OFDM systems.
Ahmed Mohamed Elshirkasi +2 more
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Convolution using a conjugate symmetry property for the generalized discrete Fourier transform
IEEE Transactions on Acoustics, Speech, and Signal Processing, 1978Often, signals which lie in a ring S are convolved using a generalized discrete Fourier transform (DFT) over an extension ring R in order to allow longer sequence lengths. In this paper, a conjugate symmetry property which generalizes the well known property of the complex DFT for real data is presented for this situation.
Dubois, Eric +1 more
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On an application of a generalization of the discrete Fourier transform to short time series
Canadian Journal of Physics, 2001A generalization of the discrete Fourier transform (DFT) is discussed. This generalization or GDFT provides a smooth interpolation between the points of the DFT. The GDFT of a sinusoidal function in a finite time window is (a) described in detail and (b) shown to coincide (aside from a simple scaling constant) with the corresponding Fourier transform,
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On the generation of non-Gaussian noise using the discrete-Fourier transform method
Proceedings of 1995 IEEE Instrumentation and Measurement Technology Conference - IMTC '95, 2002In this paper, specific time-domain noise signals with predetermined statistical characteristics, are synthesized by means of phase spectrum manipulations in the frequency domain. Each signal maintains a constant magnitude frequency response. However, different phase response distributions have been used to manipulate the phase spectrum in order to ...
L.T. Moliasa, S.S. Awad
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Mathematical background for generalized, partial, and incomplete discrete Fourier transforms
ICASSP '80. IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005We develop the theory of generalized discrete Fourier transforms (GDFTs) from the point of view of the Chinese Remainder Theorem (CRT). We give a new definition of GDFT, and apply it to the construction of multidimensional convolution algorithms which require significantly fewer multiplications and data transfer operations than the usual methods.
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Symbolic network function generation via discrete Fourier transform
IEEE Transactions on Circuits and Systems, 1984Summary: A new method of symbolic network function generation is presented. The method is based upon the theory of the discrete Fourier transform and not restricted in its application to any particular type of network analysis or network configuration. It is particularly attractive when the number of symbolic variables to be handled is not large.
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